First, let's fix one error: このお酒を飲んでみて。
Omitting the を is possible but I don't recommend it. It just doesn't sound good if a foreigner try to speak lazy Japanese.
The お before 酒（さけ）is an honorific prefix like in おなまえ (name). It's a good idea to use that prefix whenever you're talking about items, things or any nouns that belong to others.
Next, 飲んで（のんで)just means drinking. ~て みて is try to do ~.
So the sentence means "Try to drink this alcoholic drink." As far as I know the みて is written as Hiragana since 見る carries the meaning to see.
That should answer the question, which mix out of both sentences is needed in order to have a fully correct sentence.